Comments on compatibility between Conformal symmetry and Continuous higher-form symmetries

Understand

We study the compatibility between the conformal symmetry together with the unitarity and the continuous higher-form symmetries.

• We show that the d-dimensional unitary conformal field theories are not consistent with continuous p-form symmetries for certain (d,p), assuming that the corresponding conserved current is a conformal primary operator.
• We further discuss several dynamical applications of this constraint.